Brane-world singularities and asymptotics of five-dimensional bulk fluids.

We review studies on the singularity structure and asymptotic analysis of a 3-brane (flat or curved) embedded in a five-dimensional bulk filled with a 'perfect fluid' with an equation of state [Formula: see text], where [Formula: see text] is the 'pressure' and [Formula: see text] is the 'density' of the fluid, depending on the fifth space coordinate. Regular solutions satisfying positive energy conditions in the bulk exist only in the cases of a flat brane for [Formula: see text] or of AdS branes for [Formula: see text]. More cases can be found by gluing two regular brunches of solutions at the position of the brane. However, only a flat brane for [Formula: see text] leads to finite Planck mass on the brane and thus localizes gravity. In a more recent work, we showed that a way to rectify the previous findings and obtain a solution for a flat brane and a range of [Formula: see text], which is both free from finite-distance singularities and compatible with the physical conditions of energy and finiteness of four-dimensional Planck mass, is by introducing a bulk fluid component that satisfies a nonlinear equation of state of the form [Formula: see text] with [Formula: see text] and [Formula: see text]. This article is part of the theme issue 'The future of mathematical cosmology, Volume 2'.

A microscopic model for inflation from supersymmetry breaking.

We have proposed recently a framework for inflation driven by supersymmetry breaking with the inflaton being a superpartner of the goldstino, that avoids the main problems of supergravity inflation, allowing for: naturally small slow-roll parameters, small field initial conditions, absence of a (pseudo)scalar companion of the inflaton, and a nearby minimum with tuneable cosmological constant. It contains a chiral multiplet charged under a gauged R-symmetry which is restored at the maximum of the scalar potential with a plateau where inflation takes place. The effective field theory relies on two phenomenological parameters corresponding to corrections to the Kähler potential up to second order around the origin. The first guarantees the maximum at the origin and the second allows the tuning of the vacuum energy between the F- and D-term contributions. Here, we provide a microscopic model leading to the required effective theory. It is a Fayet-Iliopoulos model with two charged chiral multiplets under a second U ( 1 ) R-symmetry coupled to supergravity. In the Brout-Englert-Higgs phase of this U ( 1 ) , the gauge field becomes massive and can be integrated out in the limit of small supersymmetry breaking scale. In this work, we perform this integration and we show that there is a region of parameter space where the effective supergravity realises our proposal of small field inflation from supersymmetry breaking consistently with observations and with a minimum of tuneable energy that can describe the present phase of our Universe.

Naturalness in low-scale SUSY models and "non-linear" MSSM.

In MSSM models with various boundary conditions for the soft breaking terms ([Formula: see text]) and for a Higgs mass of 126 GeV, there is a (minimal) electroweak fine-tuning [Formula: see text] to [Formula: see text] for the constrained MSSM and [Formula: see text] for non-universal gaugino masses. These values, often regarded as unacceptably large, may indicate a problem of supersymmetry (SUSY) breaking, rather than of SUSY itself. A minimal modification of these models is to lower the SUSY breaking scale in the hidden sector ([Formula: see text]) to few TeV, which we show to restore naturalness to more acceptable levels [Formula: see text] for the most conservative case of low [Formula: see text] and ultraviolet boundary conditions as in the constrained MSSM. This is done without introducing additional fields in the visible sector, unlike other models that attempt to reduce [Formula: see text]. In the present case [Formula: see text] is reduced due to additional (effective) quartic Higgs couplings proportional to the ratio [Formula: see text] of the visible to the hidden sector SUSY breaking scales. These couplings are generated by the auxiliary component of the goldstino superfield. The model is discussed in the limit its sgoldstino component is integrated out so this superfield is realized non-linearly (hence the name of the model) while the other MSSM superfields are in their linear realization. By increasing the hidden sector scale [Formula: see text] one obtains a continuous transition for fine-tuning values, from this model to the usual (gravity mediated) MSSM-like models.

New implant designs for fracture fixation in osteoporotic bone.

Screws are one of the limiting factors for fixation of implants, particularly in poor bone quality. A class of new implants with an implant-bone-interface optimized regarding load transition by increasing the peripheral area might improve the anchorage of implants in osteoporotic bone. However, the shape of these implants requires new technologies for insertion. The goal of the work presented here was to analyze the relevant parameters regarding implant geometry and to demonstrate the effect of new procedures for their insertion. The investigation was divided into three parts: 1) implant design optimisation, 2) efficiency of cortical bone ablation, and 3) implant insertion technology. Finite element analysis (FEA) was performed to investigate the influence of the number of lobes, the radius of the outer curvature and additional milling to remove any sharp changes of section around the lobe. Opening of the cortical bone with an Er:YAG laser was studied using calf cortex from 2 to 7 mm thickness. The effect of a) pulse energy and pulse duration, b) cortical thickness, c) wet or dry boundary conditions on volume and geometry of ablated bone, time required to penetrate the cortical bone and local bone tissue damage was quantified. Pneumatic and ultrasound based insertion were compared in the third experiment. The cortical bone was prepared in the following ways: a) no opening, b) predrilling of three holes (1 mm diameter each) and c) exact pre-cutting of the whole contour. Increasing the radius of the outer curvature from 2 to 5 mm reduces the peak stresses during loading in all planes in the implant as well as in the adjacent cortical bone by about 30-40%. An increase in the number of lobes from two to three decreases the mean peak stress by about 46% (alpha < 0.001) and the range between the minimal and maximal peak stresses for different loading directions by about 83%. Penetration of cortical bone with an Er:YAG laser was possible up to a cortical thickness of 6 mm with fewer than 100 pulses. The ablation rate per pulse increased more with increasing duration than with increasing energy. Signs of bone damage such as melting were only visible when high pulse energies and durations were used. Insertion of the prototype was possible with all devices, but only when the whole contour was cut out of the cortical bone. However, the use of the ultrasound vibrator led to heating up of the tissue fluid and subsequently to water evaporation and tissue damage. Insertion of the prototype was possible with both pneumatic vibrators, but only when the whole contour was cut out of the cortical bone. New implant designs may lead to reduced stress peaks in the surrounding bone and might be inserted with the help of new insertion technologies, namely laser cutting of cortical bone and pneumatic vibration. Further studies are required to optimize these technologies prior to clinical use.

Clinical manifestations of systemic lupus erythematosus, measures of disease activity, and long-term complications.

Studies of renal involvement in systemic lupus erythematosus continue to dominate the clinical literature. Reports of the prognostic significance of both clinical and histologic parameters at the time of renal biopsy are discussed. The potential impact of anticardiolipin antibodies on the development of renal insufficiency is described. The outcome of renal transplantation in patients with systemic lupus erythematosus is assessed in a study concerned with both allograft survival and recurrence of active nephritis in the transplanted kidney. The incidence and prognosis of various features of neuropsychiatric systemic lupus erythematosus are discussed, while the search for an accurate indicator of lupus involvement of the central nervous system continues. Magnetic resonance imaging and single-photon-emission computed tomography are considered. Abnormalities of pulmonary gas exchange are featured in several reports. Features of the antiphospholipid antibody syndrome are presented, stressing predisposition to thrombosis. The definition and characteristics of systemic lupus erythematosus disease flares is discussed, in relation to several recently developed disease activity indexes. The attempt to distinguish systemic lupus erythematosus activity from infection and preeclampsia is also considered. Finally, the association of systemic lupus erythematosus with the development of cancer is discussed.